JEE Main 2020 (8 Jan, Shift 2) Maths Q59: Mean Value Theorem

Question

Let S be the set of all functions $f : [0, 1] 	o \mathbf{R}$, which are continuous on $[0, 1]$ and differentiable on $(0, 1)$. Then for every $f$ in S, there exists a $\mathrm{c} \in (0, 1)$, depending on $f$, such that :

Accepted Answer

Option 1: $|f(\mathrm{c}) - f(1)| < |f'(\mathrm{c})|$

Answer

$|f(\mathrm{c}) - f(1)| < |f'(\mathrm{c})|$

Answer

$|f(\mathrm{c}) - f(1)| < (1 - \mathrm{c})\,|f'(\mathrm{c})|$

Answer

$|f(\mathrm{c}) + f(1)| < (1 + \mathrm{c})\,|f'(\mathrm{c})|$

Answer

$\frac{f(1) - f(\mathrm{c})}{1 - \mathrm{c}} = f'(\mathrm{c})$

JEE Main 8 January 2020, Shift 2, Maths Q59

Same idea in other shifts